Modified RSA-based algorithm: a double secure approach

Abstract

Security algorithms like RSA are becoming increasingly important for communications to provide companies, organizations, and users around the world, secure applications who rely heavily on them in their daily work. Security algorithms use different acquaintances among companies which might belong to various countries or even cities. Such data should essentially be encrypted to make sure that there is security in transportation. Thus, the current research paper leads to the novel system of security for the safe transfer of data. This paper examines the general principles of encryption and focuses on the development of RSA and the complexity of the encryption key so that it becomes more secure in the applications used. In this project, we will work on the RSA algorithm by adding some complexity to the 3keys (3k). This addition will increase the security and complexity of the algorithm's speed while maintaining encryption and decryption time. The paper also presents an approach by means of public key encryption to enhance cryptographic security. Moreover, double security is provided by the algorithm of RSA. This novel RSA algorithm was investigated in MATLAB. Numerical results for the various parameters such as Mean Square Error (MSE), correlation and Bit Error Ratio (BER) were implemented for the encryption of the message. The experimental results demonstrated that the proposed algorithm for 3 keys has small error rate in the retrieval of the encoded text

Soft public key cipher

“…Based on NP-complete Knapsack cipher, the declared key encryption can be described in three methods, for the first and second method Use them not for authentication but for secrecy, whereas third method was used for authentication but not for secrecy, Shamir [3] studied the feasibility of construction, Merkle and Hellman (1978) propose a public-key system using Knapsack problem [4] by given A={a1,a2,….,an} positive integer and find the positive integer C (cipher text) by C=A.M or C= ,M={m1,m2,….mn} is represent the plaintext (Message) for example if A={10,8,17,20,15,9,6} and M={1,0,1,1,0,0,0} then C=10+17+20=47 The knapsack algorithm is one of the best algorithms to solve arbitrary instances of size n require O( ) time, in a simple Knapsack (super increasing) it solved in linear time algorithm snap (C,A): ("simple Knapsack algorithm") for i:= n down to 1 do begin if C ai then mi=1 else mi=0 C:=C-ai*mi end; if C=0 then snap:=M else " no solution exists " 2.2.1 Example given A=(1,3,5,10,22) and M=(1,1,0,1,0) then to encipher is : C=A*M=(1+3+10)=14 to decipher is : C= 1422 then m5=0 =14-22*0=14 C=1410 then m4=1 =14-10*1=4 C=45 then m3=0 =4-5*0=4…”

“…Merkle and Hellman convert it to a Trapdoor Knapsack [4], which hard to solve -choose A=(a 1 ,a 2 ,….a n ) , a i  -choose U2a n  -choose W so that gcd(U,W)=1 -compute W -1 = W (u)-1 mod U -compute E A =W*A mod U Where E A is public-key,A and W -1 are secrete to encipher is : C=E A *M To decipher : C'=w -1 *C mod U you have A and C' solve linearly form C'=A*M 2.3.1 Example: if A=(1,3,5,10) -U=20 -W=7 , gcd(7,20)=1 -then W -1 =W (U)-1 mod U =7 (7)-1 mod 7 =7 6-1 mod 7 =3 -E A =(7,1,15,10) (7*1 mod 20 , 7*3 mod 20 ,7*5 mod 20 ,7*10 mod 20) let the plaintext (M=13) then M=(1,1,0,1) to encipher is: C=E A *M=(7+1+10)=18 to decipher is: C'=C*W -1 mod U =3*18 mod 20 =14 C'=A*M=14= (1,3,5,10).M by snap(14,A*M) ,we get M=(1,1,0,1)…”

“…In the same manner of soft simple Knapsack . as example if -A=(1,3,5,10,20,80,160) -U=320 -W=7 ,gcd(7,320)=1 -compute W -1 =7 (320)-1 mod320 =7 63 mod320=183 -E A =W*A mod U =(1*7 mod 320,7*7 mod 320,5*7 mod320,10*7mod320,20*7 mod320,40*7mod320,80*7mod320,160*7 mod320) = (7,21,35,70,140,280,240,160) let H 1 =(01000111) then to encipher is: C=E A *H=701 to decipher is: C'=C*W -1 mod U =701*183 mod 320=283 C'=A*H 5 =5= (1,3,5,10,20,40,80,160…”

“…Moldtsov introduced in 1999 new mathematics to deal with the uncertainty concept of soft set Since this concept make the link between the set with the parameters of the set does not affect the current methods and be free of difficulties Since this theory has multiple applications has been previously proved by Moldtsov [1].Maji,p.k [2], from the theoretical side of soft sets, defined and studied many operations.Knapsack problem depending on the difficulty of solving that uses for either secrecy or authenticity, but not both the simple. Trapdoor Knapsack method depending on the Knapsack problem [3,4]. The signal to noise ratio (SNR) is an appropriate yardstick that uses in the characterization of the physical layer performance.…”

Key criteria of sustainable hospital refurbishment

“…An emphasis is placed on how the selected four natural environment elements (lighting, ventilation, sound quality and views) have been incorporated in hospital design through looking at the following key spaecys within building design as applied to the hospital environment. This seeks to determine the outlook of these elements within the cases vis-a-vis inferences from critical literature on designing hospital with natural environments in mind towards creating healing environments [11]. This research is exploratory in nature, and therefore a case study approach has been identified as the main research strategy.…”